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Number Theory Level 2

Find the smallest positive integer such that:

  • When divided by 10, it has a remainder of 9.
  • When divided by 9, it has a remainder of 8.
  • When divided by 8, it has a remainder of 7.
  • When divided by 7, it has a remainder of 6.


The answer is 2519.

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Alex G by Alex G , 22, USA

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1 solution

展豪 張
May 12, 2016

Adding 1 1 to this number, it will be divisible by 2 , 3 , ⋯ , 10 2,3,\cdots,10 .
l c m ( 2 , 3 , ⋯ , 10 ) = 2520 lcm(2,3,\cdots,10)=2520
The required number = 2520 − 1 = 2519 =2520-1=2519

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